General Properties of Waves

Contents

• Features of Waves
• The Wave Equation
• Transverse & Longitudinal Waves
• Wave Behaviour
• Ripple Tank

Waves & energy transfer

• Waves transfer energy without transferring matter.
• For sound waves, this means it is the wave and not the air molecules (the matter) itself that travels.
• Objects floating on water provide evidence that waves only transfer energy and not matter.
  • It is possible to see objects on the surface of the water bob up and down but not change their position.
  • This is because the wave and not the water (the matter) itself that travels.
• Waves are described as oscillations or vibrations about a fixed point.
  • For example, ripples cause particles of water to oscillate up and down.
  • Sound waves cause particles of air to vibrate back and forth.

Worked Example

The diagram below shows a toy duck bobbing up and down on top of the surface of some water, as waves pass it underneath.

Explain how the toy duck demonstrates that waves do not transfer matter.

Answer:

• The plastic duck moves up and down but does not travel with the wave along the surface of the water.
• The water waves transfer energy, but the water particles do not move.
• This means when a wave travels between two points, no matter travels with it, the points on the wave vibrate up and down about fixed positions.

• Objects floating on the water bob up and down when waves pass under them, demonstrating that there is no movement of matter in the direction of the wave, only energy.

Wave motion

• Wave motion can be illustrated by:
  • vibrations in ropes and springs
  • experiments using water waves

Waves can be shown through vibrations in ropes or springs.

• Properties of waves can be observed using water waves in a ripple tank.
• These properties include frequency, wavelength, amplitude, and wave speed.

Wave motion of water waves may be demonstrated using a ripple tank.

Features of a Wave

When describing wave motion, there are several terms which are important to know, including:

• wavefront
• amplitude
• wavelength
• frequency
• crest (peak)
• trough
• wave speed

Wavefront

• Wavefronts are a useful way of picturing waves from above.
• Each wavefront, drawn as a single line, is used to represent a single wave.
• The image below illustrates how wavefronts are visualised:
  • The arrow shows the direction the wave is moving and is sometimes called a ray.
  • The space between each wavefront represents the wavelength.
  • When the wavefronts are close together, this represents a wave with a short wavelength.
  • When the wavefronts are far apart, this represents a wave with a long wavelength.

Amplitude

• Amplitude is defined as: The maximum displacement of a wave from its undisturbed position.
• It is given the symbol A and is measured in metres (m).
• On a graph where the vertical axis is displacement, amplitude is measured from the undisturbed position to either the highest point of the wave (peak) or the lowest point (trough).

Wavelength

• Wavelength is defined as: The distance from one point on the wave to the same point on the next wave.
• In a transverse wave:
  • The wavelength can be measured from one peak to the next peak.
• In a longitudinal wave:
  • The wavelength can be measured from the centre of one compression to the centre of the next.
• Wavelength is given the symbol λ (lambda) and is measured in metres (m).
• On a graph where the horizontal axis is distance, the wavelength can be determined by measuring the distance from one point on the wave to the same point on the next wave.

Frequency

• Frequency is defined as: The number of waves passing a point in a second.
• Frequency is given the symbol f and is measured in hertz (Hz).

Crests & troughs

• A crest, or a peak, is defined as: The highest point on a wave above its undisturbed position.
• A trough is defined as: The lowest point on a wave below its undisturbed position.

Wave speed

• Wave speed is the speed at which energy is transferred through a medium.
• Wave speed is defined as: The distance travelled by a wave each second.
• The equation used to calculate wave speed is explained in The wave equation.

Worked Example

Small water waves are created in a ripple tank by a wooden bar. The wooden bar vibrates up and down hitting the surface of the water. The diagram below shows a cross-section of the ripple tank and water.

Identify the letter which shows:

a) the amplitude of a water wave.

b) the wavelength of the water wave.

Answer:

Part (a)

• Step 1: Recall the definition of amplitude.
  • Amplitude = The distance from the undisturbed position to the peak or trough of a wave.
• Step 2: Mark the undisturbed position on the wave.
  • This is the centre of the wave.

  [Diagram: The same ripple tank cross-section, but with a horizontal line drawn through the middle of the waves, labeled "UNDISTURBED POSITION".]

  
• Step 3: Identify the arrow between the undisturbed position and a peak.
  • The amplitude is shown by arrow D.

Part (b)

• Step 1: Recall the definition of wavelength.
  • Wavelength = The distance from one point on the wave to the same point on the next wave.
• Step 2: Draw lines on each horizontal arrow.
  • This helps to identify the points on the wave the arrows are referring to.

• Step 3: Identify the arrow between two of the same points on the wave.
  • The wavelength is shown by arrow C.

The wave equation

The equation used to calculate wave speed is:

v = f × λ

Where:

• v = wave speed, measured in metres per second (m/s)
• f = wave frequency, measured in hertz (Hz)
• λ = wavelength, measured in metres (m)

• Wave speed is defined as: The distance travelled by a wave each second.
• Wave speed is the speed at which energy is transferred through a medium.
• Transverse and longitudinal waves both obey the wave equation.

• For more information on how to use a formula triangle, refer to the revision note on speed & velocity.

Frequency and period

The period of a wave is defined as: The time taken for one complete oscillation to pass a fixed point.

The frequency of a wave is related to its period by the following equation:

f = 1 / T

And therefore,

T = 1 / f

Where:

• f = frequency, measured in Hz
• T = period, measured in s

Transverse waves

• Waves can exist as one of two types:
  • Transverse
  • Longitudinal

Transverse waves

• Transverse waves are defined as: Waves where the direction of vibration is at right angles to the direction of propagation.
• For a transverse wave the energy transfer is perpendicular to the wave motion.
• Mechanical transverse waves can move in solids, and on the surface of liquids but not in liquids or gases.
• Non-mechanical transverse waves can move in a vacuum.

Transverse waves can be seen in a rope when it is moved quickly up and down. Examples of waves that can be modelled as transverse are:

• Electromagnetic waves (such as radiowaves, visible light, X-rays etc)
• Ripples on the surface of water
• Seismic S-waves (secondary earthquake waves)

Longitudinal waves

• Longitudinal waves are defined as: Waves where the direction of vibration is parallel to the direction of propagation.
• For a longitudinal wave:
  • The energy transfer is in the same direction as the wave motion.
  • They can move in solids, liquids and gases.
  • They cannot move in a vacuum (since there are no particles).
• The key features of a longitudinal wave are where the points are:
  • Close together, called compressions
  • Spaced apart, called rarefactions

Longitudinal waves can be seen in a slinky spring when it is moved quickly backwards and forwards. Examples of waves that can be modelled as longitudinal waves are:

• Sound waves
• Seismic P-waves (primary earthquake waves)

Difference between transverse and longitudinal waves

Reflection, refraction & diffraction

All waves, whether transverse or longitudinal, can undergo:

• reflection at a plane surface
• refraction due to a change of speed
• diffraction through a narrow gap

• In optics, a transparent material is called a medium.
• When referring to more than one medium these are called media.
• Angles of light are measured from an imaginary line called the normal.
• The normal is always drawn perpendicular to the boundary between two media.

Reflection

• Reflection occurs when: A wave hits a boundary between two media at a plane surface and does not pass through, but instead stays in the original medium.

An identical image of the tree is seen in the water due to reflection.

Refraction

• When waves enter a different medium, their speed can change.
• This effect is called refraction and it occurs when: A wave passes a boundary between two different transparent media and undergoes a change in speed.
• When a wave refracts, as well as a change in speed, the wave also undergoes:
  • A change in wavelength (but frequency stays the same)
  • A change in direction

• Waves can change direction when moving between materials with different densities.
• The direction of the incident and refracted rays are also taken from the normal line.
• If the waves slow down, they will bunch together, causing the wavelength to decrease.
• The waves will also start to turn slightly towards the normal.
• If the waves speed up then they will spread out, causing the wavelength to increase.
• The waves will also turn slightly away from the normal.

Diffraction

• When waves pass through a narrow gap, the waves spread out.
• This effect is called diffraction.

Diffraction: when a wave passes through a narrow gap, it spreads out.

Factors affecting diffraction (Extended tier only)

• The extent of diffraction depends on the width of the gap compared with the wavelength of the waves.
• Diffraction is the most prominent when the width of the slit is approximately equal to the wavelength.
• As the gap gets bigger, the effect gradually gets less pronounced until, in the case that the gap is very much larger than the wavelength, the waves no longer spread out at all.

The size of the gap (compared to the wavelength) affects how much the waves spread out.

• Diffraction can also occur when waves curve around an edge or barrier.
• The waves spread out to fill the gap behind the object.
• The extent of this diffraction also depends upon the wavelength of the waves.
• The greater the wavelength then the greater the diffraction.

When a wave goes past the edge of a barrier, the waves can curve around it. Shorter wavelengths undergo less diffraction than longer wavelengths.

Investigating waves with a ripple tank

Ripple tanks are commonly used in experiments to demonstrate the following properties of water waves:

• Reflection at a plane surface
• Refraction due to a change in speed caused by a change in depth
• Diffraction due to a gap
• Diffraction due to an edge

• Wavefronts from the transverse water surface waves can be viewed and analysed on the screen illuminated to show below the tank.

Investigating Reflection

• Wavefronts are reflected off a metal bar (plane surface) placed in the water of the ripple tank.
• When the bar is placed at an angle to the wavefronts of the waves generated by the paddle, they reflect according to the Law of reflection.

Incident wavefronts are reflected at 90 degrees against a barrier.

Wavefronts of incident and reflected waves form right angles to each other.

Investigating refraction

• Refraction can be shown by placing a glass block in the tank.
• The glass block should sit below the surface of the water and cover only some of the tank floor.
• The depth of water becomes shallower where the glass block is placed.
• Since speed depends on depth, the ripples slow down when travelling over the block.

When water waves travel from deep areas to shallow areas they slow down.

Investigating diffraction

• Diffraction can be shown in a ripple tank by placing small barriers with a gap or an edge in the tank.
• The amount of Diffraction that occurs can be changed by changing the wavelength of the waves compared to the gap size.

When the gap size is bigger than the wavelength less diffraction occurs and the waves spread out less after passing through.

Changing the wavelength of waves in the ripple tank

• The motor creates the up-and-down movement of the paddle.
• The frequency of the motor affects the wavelength of the waves generated by the paddle.
• The diagram below shows how the wavelengths differ with frequency in a ripple tank.
• The higher the frequency of the motor, the shorter the wavelength.
• The lower the frequency of the motor, the longer the wavelength.

Ripple tank patterns for low and high-frequency vibration.